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Islamic Azad University, Shahrekord Branch&Persian Gulf University, Bushehr, Iran
Abstract
In this paper we introduce the notion of generalized state coannihilators in state residuated lattices. We establish a connection between generalized state coannihilators and Galois connection. If A is a state residuated lattice, we show that the set of filters forms a Heyting algebra in which the relative pseudo-complement of G with respect to F is (F : G)ν. Also, we show that the set of state coannihilator filters form a Boolean lattice. Ultimately, we characterize generalized state coannihilators in terms of state prime filters and state minimal prime filters.
Karimi Shahmarvandi,A , Rasouli,S and Khaksar Haghani,F . (2026). Generalize state coannihilators in state residuated lattices. Mathematical Research, 9(3), 178-213.
MLA
Karimi Shahmarvandi,A , , Rasouli,S , and Khaksar Haghani,F . "Generalize state coannihilators in state residuated lattices", Mathematical Research, 9, 3, 2026, 178-213.
HARVARD
Karimi Shahmarvandi A, Rasouli S, Khaksar Haghani F. (2026). 'Generalize state coannihilators in state residuated lattices', Mathematical Research, 9(3), pp. 178-213.
CHICAGO
A Karimi Shahmarvandi, S Rasouli and F Khaksar Haghani, "Generalize state coannihilators in state residuated lattices," Mathematical Research, 9 3 (2026): 178-213,
VANCOUVER
Karimi Shahmarvandi A, Rasouli S, Khaksar Haghani F. Generalize state coannihilators in state residuated lattices. Mathematical Research. 2026;9(3):178-213 (In Persian).
Mathematical Research